primaryIdeal
Zero dimensional ideal associated primary ideal. See algorithm
mas.masring.DIPIDEAL#DIRLPI.
- Parameters:
P
- prime ideal associated to this- Returns:
- primary ideal of this with respect to the associated pime ideal P
Serializable
, Comparable<Ideal<C>>
protected final GroebnerBaseAbstract<C>
private static final boolean
protected final SquarefreeAbstract<C>
protected boolean
protected boolean
protected PolynomialList<C>
private static final org.apache.logging.log4j.Logger
protected boolean
Ideal(GenPolynomialRing<C> ring)
Ideal(GenPolynomialRing<C> ring,
List<GenPolynomial<C>> F)
Ideal(GenPolynomialRing<C> ring,
List<GenPolynomial<C>> F,
boolean gb)
Ideal(GenPolynomialRing<C> ring,
List<GenPolynomial<C>> F,
boolean gb,
boolean topt)
Ideal(PolynomialList<C> list)
Ideal(PolynomialList<C> list,
boolean gb)
Ideal(PolynomialList<C> list,
boolean gb,
boolean topt)
Ideal(PolynomialList<C> list,
boolean gb,
boolean topt,
GroebnerBaseAbstract<C> bb)
Ideal(PolynomialList<C> list,
boolean gb,
boolean topt,
GroebnerBaseAbstract<C> bb,
Reduction<C> red)
Ideal(PolynomialList<C> list,
boolean gb,
GroebnerBaseAbstract<C> bb)
Ideal(PolynomialList<C> list,
boolean gb,
GroebnerBaseAbstract<C> bb,
Reduction<C> red)
Ideal(PolynomialList<C> list,
GroebnerBaseAbstract<C> bb,
Reduction<C> red)
annihilator(Ideal<C> H)
int
int
constructUnivariate(int i)
protected boolean
boolean
boolean
contains(GenPolynomial<C> b)
boolean
contains(List<GenPolynomial<C>> B)
protected boolean
containsHT(Set<Integer> H,
List<GenPolynomial<C>> G)
static <C extends GcdRingElem<C>>
IdealWithUniv<C>
contraction(IdealWithUniv<Quotient<C>> eid)
copy()
void
doGB()
void
boolean
extension(GenPolynomialRing<C> efac)
extension(QuotientRing<C> qfac)
GB()
getList()
getONE()
getRing()
getZERO()
int
hashCode()
infiniteQuotient(Ideal<C> H)
int
infiniteQuotientExponent(GenPolynomial<C> h,
Ideal<C> Q)
inverse(GenPolynomial<C> h)
boolean
isAnnihilator(Ideal<C> H,
Ideal<C> A)
boolean
isAnnihilator(GenPolynomial<C> h,
Ideal<C> A)
boolean
boolean
isGB()
boolean
boolean
isNormalPositionFor(int i,
int j)
boolean
isONE()
boolean
boolean
isRadical(IdealWithUniv<C> ru)
boolean
boolean
isUnit(GenPolynomial<C> h)
boolean
isZERO()
boolean
boolean
normalform(GenPolynomial<C> h)
normalform(List<GenPolynomial<C>> L)
normalPositionFor(int i,
int j,
List<GenPolynomial<C>> og)
(package private) IdealWithUniv<C>
normalPositionForChar0(int i,
int j,
List<GenPolynomial<C>> og)
(package private) IdealWithUniv<C>
normalPositionForCharP(int i,
int j,
List<GenPolynomial<C>> og)
int[]
int[]
permContraction(IdealWithUniv<Quotient<C>> eideal)
static <C extends GcdRingElem<C>>
IdealWithUniv<C>
permutation(GenPolynomialRing<C> oring,
IdealWithUniv<C> Cont)
power(int d)
primaryIdeal(Ideal<C> P)
product(GenPolynomial<C> b)
quotient(GenPolynomial<C> h)
radical()
sum(GenPolynomial<C> b)
sum(List<GenPolynomial<C>> L)
toScript()
toString()
zeroDimDecompositionExtension(List<GenPolynomial<C>> upol,
List<GenPolynomial<C>> og)
zeroDimElimination(List<IdealWithUniv<C>> pdec)
ring
- polynomial ringring
- polynomial ringF
- list of polynomialsring
- polynomial ringF
- list of polynomialsgb
- true if F is known to be a Groebner Base, else falsering
- polynomial ringF
- list of polynomialsgb
- true if F is known to be a Groebner Base, else falsetopt
- true if term order is optimized, else falselist
- polynomial listlist
- polynomial listbb
- Groebner Base enginered
- Reduction enginelist
- polynomial listgb
- true if list is known to be a Groebner Base, else falselist
- polynomial listgb
- true if list is known to be a Groebner Base, else falsetopt
- true if term order is optimized, else falselist
- polynomial listgb
- true if list is known to be a Groebner Base, else falsebb
- Groebner Base enginered
- Reduction enginelist
- polynomial listgb
- true if list is known to be a Groebner Base, else falsebb
- Groebner Base enginelist
- polynomial listgb
- true if list is known to be a Groebner Base, else falsetopt
- true if term order is optimized, else falsebb
- Groebner Base enginelist
- polynomial listgb
- true if list is known to be a Groebner Base, else falsetopt
- true if term order is optimized, else falsebb
- Groebner Base enginered
- Reduction enginecompareTo
in interface Comparable<C extends GcdRingElem<C>>
L
- other Ideal.! id.isONE()
.B
- idealb
- polynomialB
- list of polynomialsB
- idealb
- polynomialL
- list of polynomialsB
- idealb
- polynomialBl
- list of idealsB
- idealR
- polynomial ringR
- polynomial ringename
- variables for the elimination ring.h
- polynomialH
- idealh
- polynomialh
- polynomialQ
- quotient this : h^\infinityh
- polynomialh
- polynomialh
- polynomialH
- idealH
- ideald
- integerh
- polynomialL
- polynomial listh
- polynomialh
- polynomialA
- idealH
- idealH
- idealA
- idealh
- polynomialh
- polynomialS
- is a set of independent variables.U
- is a set of variables of unknown status.M
- is a list of maximal sets of independent variables.H
- index set.G
- list of polynomials.v
- index array.H
- index set.i
- variable index.ru
- ideal with univariate polynomialsupol
- list of univariate polynomialsog
- list of other generators for the idealL
- intersection of ideals G_i with ideal(G) subseteq cap_i(
ideal(G_i) ) and all minimal univariate polynomials of all G_i
are irreduciblei
- first variable indexj
- second variable indexog
- other generators for the ideali
- first variable indexj
- second variable indexog
- other generators for the ideali
- first variable indexj
- second variable indexog
- other generators for the ideali
- first variable indexj
- second variable indexP
- prime ideal associated to thispdec
- list of prime ideals G_ipdec
- list of prime ideals G_i with no field extensionsL
- list of primary components G_ivars
- list of variables for a polynomial ring for extensionefac
- polynomial ring for extensionqfac
- quotient polynomial ring for extensioneideal
- extension ideal of this.eid
- extension ideal of this.oring
- polynomial ring to which variables are back permuted.Cont
- ideal to be permutedL
- intersection of ideals G_i with ideal(G) eq cap_i(ideal(G_i) )